Question

Crude oil biodegradation. Refer to the Journal of Petroleum
Geology (April, 2010) study of the environmental factors
associated with biodegradation in crude oil reservoirs,
Exercise 2.18 (p. 37). Recall that amount of dioxide (milligrams/
liter) and presence/absence of crude oil was determined
for each of 16 water specimens collected from a mine
reservoir. The data are repeated in the accompanying table.
a. Find the mean dioxide level of the 16 water specimens.
Interpret this value.
b. Find the median dioxide level of the 16 water specimens.
Interpret this value.
c. Find the mode of the 16 dioxide levels. Interpret this
value.
d. Find the median dioxide level of the 10 water specimens
with no crude oil present.
e. Find the median dioxide level of the 6 water specimens
with crude oil present.

BIODEG
MINITAB Output for Exercise 2.33
Dioxide Amount Crude Oil Present
3.3 No
0.5 Yes
1.3 Yes
0.4 Yes
0.1 No
4.0 No
0.3 No
0.2 Yes
2.4 No
2.4 No
1.4 No
0.5 Yes
0.2 Yes
4.0 No
4.0 No
4.0 No

Answer 1

Answer:

a)

The mean of a set of observations is defined as their sum, divided by the number of observations _3.3+0.5+1.3+0.4+0.1+4 +0.3+0.2 + ... 4.0+ 4.0+4.0 16 = 1.81

Interpretation:

The mean indicates the central position of the data. Here, the mean 181 indicates the average of the dioxide amount present in 16 water specimens collected from a mine reservoir.

b)

Median of a set of observations is the value of the middle most item when they are arranged in order of magnitude. Here, the total number of observations is 16, which is an even number. Hence, the median is the average of the middle two numbers of the arranged data. The data are arranged in ascending order as given below: 0.1, 0.2, 0.3, 0.5, 0.5, 1.3, 1.4, 2.4, 2.4, 3.3, 4.0, 4.0, 4.0. The median of the given dataset is given below: 1.3+1.4 2.7 = 1.35

Interpretation:

The number of observations smaller than median is same as the number greater than it. Thus, median divides the observation into two equal parts. Hence, half of the dioxide levels is below 1.35 and half is above 1.35.

c)

Mode of a given set of observations is that value which occurs with the maximum frequency. Hence, for the given data, the mode is 4.

Interpretation:

The amount of dioxide which occurs frequently is 4

d)

Median of a set of observations is the value of the middle most item when they are arranged in order of magnitude. Here, the total number of observations is 10, which is an even number. Hence, the median is the average of the middle two numbers of the arranged data. The data are arranged in ascending order as given below: 0.1, 0.3, 1.4, 2.4, 2.4, 3.3, 4.0, 4.0, 4.0.4.0. The median of the given dataset is given below: 2.4+3.3 - 2.85

e)

Median of a set of observations is the value of the middle most item when they are arranged in order of magnitude. Here, the total number of observations is 6, which is an even number. Hence, the median is the average of the middle two numbers of the arranged data. The data are arranged in ascending order as given below: 0.2, 0.2, 0.4, 0.5, 0.5, 1.3 The median of the given dataset is given below: 0.4+0.2 _ 0.9 = 0.45